Many mathematicians are aware of some of the dramatic interactions between ergodic
theory and other parts of the subject, notably Ramsey theory, infinite combinatorics, and …

More specifically, let G bea real Lie group (all groups in this paper are assumed to be
second-countable) with the Lie algebra 15, F a discrete subgroup of G and n" GF\G the …

Let G be a connected Lie group and Γ be a lattice in G; that is, Γ is a discrete subgroup of G
such that G/Γ admits a finite G-invariant measure. Let {gt} teP be a oneparameter subgroup …

The study of geodesic flows on homogeneous spaces is an area of research that has
recently yielded some fascinating developments. This book focuses on many of these, with …

Let G be a Lie group and Γ be a discrete subgroup. We show that if {μn} is a convergent
sequence of probability measures on G/Γ which are invariant and ergodic under actions of …

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial
tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We …

Publisher Summary This chapter focuses on the discrete subgroups and the ergodic theory.
It presents the formulation of results and conjectures. The results on the behavior of …

Let G be a connected Lie group, F be a lattice in G and U={ut},~ R be a unipotent one-
parameter subgroup of G, viz. Adu is a unipotent linear transformation for all u~ U. Consider …

Publisher Summary This chapter presents an exposition of homogeneous dynamics—that is,
the dynamical and ergodic properties of actions on the homogeneous spaces of Lie groups …

We prove effective equidistribution, with polynomial rate, for large closed orbits of
semisimple groups on homogeneous spaces, under certain technical restrictions (notably …